Pre-AP Algebra 2 Goal(s):

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Presentation transcript:

Pre-AP Algebra 2 Goal(s): Analyze the effects on a graph when the parameters of the equation are changed Vertical shifts Horizontal shifts Reflections Vertical stretches or compressions Horizontal stretches or compressions

Vertical Shifts Given a graph f(x): Compare it to f(x) + 3:

Vertical Shifts Given a graph f(x): Compare it to f(x) – 2:

Vertical Shifts In general, a graph f(x) + k is the graph of f(x) shifted up(+) or down(-) k units. So f(x) + 5 is shifted up 5 units from f(x) and f(x) – 8 is shifted down 8 units from f(x).

Horizontal Shifts Given a graph f(x): Compare it to f(x + 3):

Horizontal Shifts Given a graph f(x): Compare it to f(x – 1):

Horizontal Shifts In general, a graph f(x - h) is the graph of f(x) shifted left(+) or right(-) h units. So f(x + 5) is shifted left 5 units from f(x) and f(x – 8) is shifted right 8 units from f(x).

Reflection over the x-axis Given a graph f(x): Compare it to -f(x): In general, a graph -f(x) is the graph of f(x) reflected over the x-axis.

Vertical Stretch or Compression Given a graph f(x): Compare it to 2f(x):

Vertical Stretch or Compression Given a graph f(x): Compare it to 1 3 f(x):

Vertical Stretch or Compression In general, a graph af(x) is the graph of f(x) vertically stretched or compressed. If a<1, there is a compression If a >1, there is a stretch So 1 2 f(x) is vertically compressed by a factor of ½ and 4f(x) is vertically stretched by a factor of 4

Horizontal Stretch or Compression Given a graph f(x): Compare it to f(2x):

Horizontal Stretch or Compression Given a graph f(x): Compare it to f( 1 3 x):

Horizontal Stretch or Compression In general, a graph f(bx) is the graph of f(x) horizontally stretched or compressed. If b<1, there is a compression If b >1, there is a stretch So f( 1 2 x) is horizontally compressed by a factor of ½ and f(4x) is horizontally stretched by a factor of 4

Function Transformations Given a function, f(x) the following are general transformations of the graph of the function: -af(b(x-h))+k h  horizontal shift (left or right) b  horizontal stretch or compression a  vertical stretch or compression (in front of function)  reflection over x-axis k  vertical shift (up or down)